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The aim of this paper is to introduce the notion of Perov–Ćirić–Prešić-type Θ -contractions and to obtain some generalized fixed point theorems in the setting of vector-valued metric spaces. We derive some fixed point results as consequences of our main results. A nontrivial example is also provided to support the validity of our established results. As an application, we investigate the solution of a semilinear operator system in Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the fixed point results in the context of complex-valued metric spaces can be obtained as a consequence of corresponding existing results in the literature in the setting of associative metric spaces. In particular, we deduce that any complex metric space is a special case of cone metric spaces with a normal cone. [ABSTRACT FROM AUTHOR]

In this paper, we propose hybrid implicit and explicit viscosity iterative algorithms for solving general hierarchical fixed-point problems for a countable family of non-expansive mappings in uniformly smooth Banach spaces. These hybrid viscosity algorithms are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under suitable conditions. Our results extend, improve, supplement and develop the recent results in the literature. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to introduce and analyze hybrid viscosity methods for a general system of variational inequalities (GSVI) with hierarchical fixed point problem constraint in the setting of real uniformly convex and 2-uniformly smooth Banach spaces. Here, the hybrid viscosity methods are based on Korpelevich's extragradient method, viscosity approximation method, and hybrid steepest-descent method. We propose and consider hybrid implicit and explicit viscosity iterative algorithms for solving the GSVI with hierarchical fixed point problem constraint not only for a nonexpansive mapping but also for a countable family of nonexpansive mappings in X, respectively. We derive some strong convergence theorems under appropriate conditions. Our results extend, improve, supplement, and develop the recent results announced by many authors. [ABSTRACT FROM AUTHOR]

We establish some fixed point theorems for a-admissible mappings in the context of metric-like space via various auxiliary functions. In particular, we prove the existence of a fixed point of the generalized Meir-Keeler type α-ø-contractive self-mapping f defined on a metric-like space X. The given results generalize, improve, and unify several fixed point theorems for the generalized cyclic contractive mappings that have appeared recently in the literature. [ABSTRACT FROM AUTHOR]

We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. [ABSTRACT FROM AUTHOR]

Based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method, we propose implicit and explicit iterative schemes for computing a common element of the solution set of a system of variational inequalities and the set of zeros of an accretive operator, which is also a unique solution of a variational inequality. Under suitable assumptions, we study the strong convergence of the sequences generated by the proposed algorithms. The results of this paper improve and extend several known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of ρ-nonexpansive mappings defined on a nonempty, ρ-closed and ρ-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal. MSC: Primary 47H09; Secondary 46B20, 47H10. [ABSTRACT FROM AUTHOR]

In the setting of quasimetric spaces, we prove some new results on the existence of fixed points for contractive type maps with respect to Q-function. Our results either improve or generalize many known results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this article is to establish some fixed point results for fuzzy mappings and derive some corresponding multivalued mappings results of literature. For this purpose, we define some new and generalized contractions in the setting of b-metric spaces. As applications, we find solutions of integral inclusions by our obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define generalized ( α β - ψ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / (ι) = − ρ 1 (ι) ϑ (ι) + ρ 2 (ι) L (ϑ (ι − ς (ι))) + ρ 3 (ι) ϑ / (ι − ς (ι)) , where ρ 1 (ι) , ρ 2 (ι) are continuous, ρ 3 (ι) is continuously differentiable and ς (ι) > 0 , for all ι ∈ R and is twice continuously differentiable. [ABSTRACT FROM AUTHOR]

Formulation of uncertainty Volterra integrodifferential equations (VIDEs) is very important issue in applied sciences and engineering; whilst the natural way to model such dynamical systems is to use the fuzzy approach. In this work, we present and prove the existence and uniqueness of four solutions of fuzzy VIDEs based on the Hausdorff distance under the assumption of strongly generalized differentiability for the fuzzy-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported fuzzy sets in . In addition to that, we utilize and prove the characterization theorem for solutions of fuzzy VIDEs which allow us to translate a fuzzy VIDE into a system of crisp equations. The proof methodology is based on the assumption of the generalized Lipchitz property for each nonlinear term appears in the fuzzy equation subject to the specific metric used, while the main tools employed in the analysis are founded on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Formulation of uncertainty Volterra integrodifferential equations (VIDEs) is very important issue in applied sciences and engineering; whilst the natural way to model such dynamical systems is to use the fuzzy approach. In this work, we present and prove the existence and uniqueness of four solutions of fuzzy VIDEs based on the Hausdorff distance under the assumption of strongly generalized differentiability for the fuzzy-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported fuzzy sets in l . In addition to that, we utilize and prove the characterization theorem for solutions of fuzzy VIDEs which allow us to translate a fuzzy VIDE into a system of crisp equations. The proof methodology is based on the assumption of the generalized Lipchitz property for each nonlinear term appears in the fuzzy equation subject to the specific metric used, while the main tools employed in the analysis are founded on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed. [ABSTRACT FROM AUTHOR]

This paper investigates some nonlinear third-order ordinary differential equations and inclusions with anti-periodic type integral boundary conditions and multi-strip boundary conditions. To establish the existence results for the given problems, we apply standard tools of fixed point theory for single-valued and multi-valued problems. The results are illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

This paper investigates some nonlinear third-order ordinary differential equations and inclusions with anti-periodic type integral boundary conditions and multi-strip boundary conditions. To establish the existence results for the given problems, we apply standard tools of fixed point theory for single-valued and multi-valued problems. The results are illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

We introduce Mann-type extragradient methods for a general system of variational inequalities with solutions of a multivalued variational inclusion and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type extragradient methods are based on Korpelevich's extragradient method and Mann iteration method. We first consider and analyze a Mann-type extragradient algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another Mann-type extragradient algorithm in a smooth and uniformly convex Banach space. Under suitable assumptions, we derive some weak and strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature. [ABSTRACT FROM AUTHOR]

F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α -fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α -fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature. [ABSTRACT FROM AUTHOR]